This section is intended to introduce various aspects of the art, which may be associated with embodiments of the disclosed techniques. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the disclosed techniques. Accordingly, it should be understood that this section is to be read in this light, and not necessarily as admissions of prior art.
Three-dimensional (3D) model construction and visualization have been widely accepted by numerous disciplines as a mechanism for analyzing, communicating, and comprehending complex 3D datasets. Examples of structures that can be subjected to 3D analysis include the earth's subsurface, facility designs and the human body, to name just three examples.
The ability to easily interrogate and explore 3D models is one aspect of 3D visualization. Relevant models may contain both 3D volumetric objects and co-located 3D polygonal objects. Examples of volumetric objects are seismic volumes, MRI scans, reservoir simulation models, and geologic models. Interpreted horizons, faults and well trajectories are examples of polygonal objects. In some cases, there is a need to view the volumetric and polygonal objects concurrently to understand their geometric and property relations. If every cell of the 3D volumetric object is rendered fully opaque, other objects in the scene will of necessity be occluded, and so it becomes advantageous at times to render such volumetric objects with transparency so that other objects may be seen through them. These 3D model interrogation and exploration tasks are important during exploration, development and production phases in the oil and gas industry. Similar needs exist in other industries.
3D volumetric objects may be divided into two basic categories: structured grids and unstructured grids. Those of ordinary skill in the art will appreciate that other types of grids may be defined on a spectrum between purely structured grids and purely unstructured grids. Both structured and unstructured grids may be rendered for a user to explore and understand the associated data. There are large numbers of known volume rendering techniques for structured grids. Many such known techniques render a full 3D volume with some degree of transparency, which enables the user to see through the volume. However, determining relations of 3D object properties is difficult, because it is hard to determine the exact location of semi-transparent data.
A first known way to view and interrogate a 3D volume is to render a cross-section through the 3D volume. The surface of the intersection between the cross-section and the 3-D volume may be rendered as a polygon with texture-mapped volume cell properties added thereto. In the case of a structured grid such as seismic or a medical scan, the user can create cross-sections along one of the primary directions: XY (inline or axial), XZ (cross-line or coronal) and YZ (time slice or sagittal). A traditional cross-section spans the extent of the object. In this case other objects such as horizons, wells or the like are partially or completely occluded and it is difficult to discern 3D relationships between objects.
This effect is shown in FIG. 1, which is a 3D graph 100 of a subsurface region. The graph 100, which may provide a visualization of 3D data for a structured grid or an unstructured grid, shows a first cross-section 102, a second cross-section 104, a third cross-section 106 and a fourth cross-section 108. Each of the four cross-sections shown in FIG. 1 is chosen to allow a user to see data in a physical property model that comprises data representative of a property of interest. However, a first horizon 110 and a second horizon 112, as well as data displayed on cross-sections 102, 104 and 106 which also may be of interest to a user, are mostly obscured or occluded by the visualizations of the four cross-sections.
A ribbon section, also called an arbitrary vertical cross-section, is one attempt to make traditional cross-sectional visual representations more flexible. To create a ribbon section, the user digitizes a polyline on one face of a volume bounding box. The polyline is extruded vertically through the volume creating a curtain or ribbon, and the volumetric data from the intersection of the ribbon with the volume is painted on the curtain surface.
This concept of arbitrary vertical cross-sections (i.e. ribbon sections) is depicted in FIG. 2, which is a 3D graph 200 of a subsurface region showing an arbitrary vertical cross-section defined by a polyline having two segments. The graph 200, which may provide a visualization of 3D data for a structured grid or an unstructured grid, shows an arbitrary vertical cross-section defined by a first line segment 202 and a second line segment 204. Although the arbitrary cross-section shown in FIG. 2 is less intrusive than the cross-sections shown in FIG. 1, portions of a first horizon 206 and a second horizon 208 are still occluded as long as the arbitrary cross-section is displayed.
U.S. Pat. Nos. 7,098,908 and 7,248,258 disclose a system and method for analyzing and imaging 3D structured grids using ribbon sections. In one disclosed system, a ribbon section is produced which may include a plurality of planes projected from a polyline. The polyline includes one or more line segments preferably formed within a plane. The projected planes intersect the 3D volume data set and the data located at the intersection may be selectively viewed. The polyline may be edited or varied by editing or varying the control points which define the polyline. Physical phenomena represented within the three-dimensional volume data set may be tracked. A plurality of planes may be successively displayed in the three-dimensional volume data set from which points are digitized related to the structure of interest to create a spline curve on each plane. The area between the spline curves is interpolated to produce a surface representative of the structure of interest, which may for example be a fault plane described by the three-dimensional volume data set. This may allow a user to visualize and interpret the features and physical parameters that are inherent in the three-dimensional volume data set.
Some 3D visualization techniques are suitable for grid structures that fall between fully structured grids and fully unstructured grids. One such visualization technique relates to the use of reservoir simulation grids based on geologic models.
As used herein, the term “geologic model” refers to a model that is topologically structured in I,J,K space but geometrically varied. A geologic model may be defined in terms of nodes and cells. Geologic models can also be defined via pillars (columnar cells or 2.5D grid—i.e. a 3D grid extruded from a 2D grid). A geologic model may be visually rendered as a shell (i.e. a volume with data displayed only on outer surfaces).
As noted, a geologic model may be thought of as an intermediate step between completely structured and completely unstructured grids. In its simplest form, a geologic model may comprise a structured grid with deformed geometry. In a geologic model, cells may be uniquely addressable, but their geometries are not entirely implicit. Because of deformation, a cell's corner vertices cannot be calculated from just the grid origin and unit vectors along with the cell's indices. However, each cell is still a polyhedron with six faces. An index may be used to find its neighbors. Each cell (except the boundary faces) shares six faces with other cells, and shares eight corners with other cells. Neighboring cells sharing a vertex may also be addressed. Those of ordinary skill in the art will appreciate that there may be variations on this basic definition of a geologic model. For example, a geologic model may comprise keyed out cells, faults and pinch outs. However, the basic indices still apply and the majority of cells comprise six-faced polyhedrons. In addition, reservoir simulation grids that are based on geologic models may retain (i, j, k) cell indices, while explicitly storing cell geometries.
U.S. Pat. No. 6,106,561 discloses a reservoir simulation grid that is based on a geologic model. The grid is produced by a simulation gridding program that includes a structured gridder. The structured gridder includes a structured areal gridder and a block gridder. The structured areal gridder builds an areal grid on an uppermost horizon of an earth formation by performing the following steps: (1) building a boundary enclosing one or more fault intersection lines on the horizon, and building a triangulation that absorbs the boundary and the faults; (2) building a vector field on the triangulation; (3) building a web of control lines and additional lines inside the boundary which have a direction that corresponds to the direction of the vector field on the triangulation, thereby producing an areal grid; and (4) post-processing the areal grid so that the control lines and additional lines are equi-spaced or smoothly distributed. The block gridder of the structured gridder will drop coordinate lines down from the nodes of the areal grid to complete the construction of a three dimensional structured grid. A reservoir simulator will receive the structured grid and generate a set of simulation results which are displayed on a 3D viewer for observation by a workstation operator.
U.S. Pat. No. 6,018,497 describes a system having a single grid made up of a mixture of structured and unstructured elements. Unstructured cells are used around wells because there is higher resolution data in these areas. Other areas are represented by regular grid cells. The software generates (i, j, k) indices for the whole grid, so at the end the grid has the characteristics of a structured grid and it may be classified as a semi-structured grid. In particular, a method and apparatus generates grid cell property information that is adapted for use by a computer simulation apparatus which simulates properties of an earth formation located near one or more wellbores. An interpretation workstation includes at least two software programs stored therein: a first program and a second simulation program which is responsive to output data produced from the first program for generating a set of simulation results. The set of simulation results are displayed on a workstation display monitor of the workstation. The first program will: receive well log and seismic data which indicates the location of each layer of a formation near a wellbore, and then grid each layer of the formation, the grid being comprised of a plurality of cells. The first program will then generate more accurate data associated with each cell, such as the transmissibility of well fluid through each cell. The more accurate data for each cell originating from the first program will be transmitted to the second simulation program. The second simulation program will respond to the more accurate data for each cell of the grid from the first program by generating a set of more accurate simulation results for each cell of the grid. The second simulation program will overlay the more accurate simulation result for each cell onto each of the corresponding cells of the grid which is being generated and displayed on the workstation display by the first program. As a result, the workstation will display each layer of the earth formation where each layer is gridded with a plurality of cells, and each cell has its own particular color which corresponds in numerical value to the particular more accurate simulation result (e.g., pressure or saturation) that corresponds to that cell.
Another known attempt to provide a 3D visualization is for a user to render one or more subsets of 3D structured grid data. This technique is called volume probing or volume roaming (SGI OpenGL Volumizer Programmer's Guide) or alternatively just probing, as discussed in U.S. Pat. Nos. 6,765,570 and 6,912,468. The subsets may be created, resized, shaped, and moved interactively by the user within the whole 3D volume data set. As a subset changes shape, size, or location in response to user input, the image is re-drawn at a rate so as to be perceived as real-time by the user. In this manner, the user is allegedly able to visualize and interpret the features and physical parameters that are inherent in the 3D volume data set.
FIG. 3 is a 3D graph 300 of a subsurface region showing an area of interest identified by a 3-D data subset. The graph 300, which may provide a visualization of 3D data for a structured grid or an unstructured grid, shows a 3D data subset 302. A first horizon 304 and a second horizon 306 are also shown. In the graph 300, the second horizon 306 is partially occluded by the 3D data subset 302. Because of the manner in which the data subset 302 was selected, it cannot easily be moved to reveal the occluded portion of the second horizon 306.
Another approach to rendering 3D object properties is the use of isosurfaces, which represent data points having the same or similar property values. An isosurface is a 3D analog to a contour line on a map, which connects points of the same elevation. Contour lines on a 2D map allow an understanding of the location of mountains and valleys, even though the map is flat. Similarly, isosurfaces can help provide an understanding of property distribution in a 3D volume. There are number of ways to create isosurfaces. One such algorithm is known as a marching cube algorithm. This technique, however, is not widely used to visualize seismic data, because seismic property values change by a large amount every time a sedimentary layer is encountered. If isosurfaces are rendered in seismic data, the result would be a visualization resembling a large number of pancake-like surfaces stacked on top each other. Accordingly, isosurfaces are not commonly used in the oil and gas industry.
FIG. 4 is an isosurface rendering 400 of an unstructured grid. The isosurface rendering 400 comprises a first isosurface 402, a second isosurface 404, and third isosurfaces 406. Each of the first isosurface 402, the second isosurface 404, and the third isosurfaces 406 represent surfaces, each of which represents a common parameter value in a 3D region.
Another technique for displaying data corresponding to a 3D region is volume rendering a space with different attributes corresponding to different values of a parameter of interest. For example, different regions of the 3D region may be shaded in different colors based on variations in a parameter of interest.
FIG. 5 is a volume rendering 500 of an unstructured grid. The volume rendering 500 comprises a first region 502 and a second region 504. The first region 502 and the second region 504 are shaded differently to indicate that the value of a parameter of interest is in a different range in the first region 502 relative to the second region 504.
Another known method of producing visualizations of data represented in a structured grid relates to the use of a probe. A user can quickly explore a 3D volume by moving the probe. U.S. Pat. No. 6,765,570 discloses a system and method for analyzing and imaging 3D volume data sets using a 3D sampling probe. According to a disclosed system, a number of sampling probes can be created, shaped, and moved interactively by the user within the whole 3D volume data set. As the sampling probe changes shape, size, or location in response to user input, the image is re-drawn at a rate so as to be perceived as real-time by the user. In this manner, the user is allegedly able to visualize and interpret the features and physical parameters that are inherent in the 3D volume data set.
U.S. Pat. No. 6,912,468 discloses a method and apparatus for contemporaneous utilization of a higher order probe in pre-stack and post-stack seismic domains. The disclosed method includes initiating a higher order probe at a three-dimensional coordinate in a post-stack seismic volume and instantiating a pre-stack seismic data content for the higher order probe.
A publication by Speray, D. and Kennon, S., entitled “Volume Probe: Interactive Data Exploration on Arbitrary Grids”, Computer Graphics, November, 1990 describes a technique for probing an unstructured grid using one or three sheets where a sheet is a planar cutting surface that may have limited extents. This functionality is very limiting in that the planar sheets can not represent real objects and probing with real objects is a significant advantage to users.
U.S. Patent Application Publication No. 2009/0303233 describes a system and method for probing geometrically irregular grids. The disclosure specifically relates to systems and methods for imaging a 3D volume of geometrically irregular grid data. Various types of probes and displays are used to render the geometrically irregular grid data, in real-time, and analyze the geometrically irregular grid data. The grids described require topologically regular I,J,K indexing. This indexing is a requirement for the described probing technique, which significantly limits the types of data on which the described method can operate.
Thus, numerous techniques exist for providing visualizations for data in the context of a structured grid. A system and method of providing visualizations for data organized in an unstructured grid is desirable.